## 42 Citations

Morphisms Cohomology and Deformations of Hom-algebras

- MathematicsJournal of Nonlinear Mathematical Physics
- 2018

The purpose of this paper is to define cohomology complexes and study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We discuss infinitesimal deformations,…

Simultaneous deformations and Poisson geometry

- MathematicsCompositio Mathematica
- 2015

We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an $L_{\infty }$-algebra, which we construct explicitly. Our machinery…

A pr 2 01 8 C ohomology and Deformations of n-Lie algebra morphisms

- Mathematics
- 2018

The study of n-Lie algebras which are natural generalization of Lie algebras is motivated by Nambu Mechanics and recent developments in String Theory and M-branes. The purpose of this paper is to…

Rota-Baxter operators and related structures on anti-flexible algebras

- Mathematics
- 2021

In this paper, we first construct a graded Lie algebra which characterizes Rota-Baxter operators on an anti-flexible algebra as Maurer-Cartan elements. Next, we study infinitesimal deformations of…

Review of deformation theory I: Concrete formulas for deformations of algebraic structures

- Mathematics
- 2019

In this review article, first we give the concrete formulas of representations and cohomologies of associative algebras, Lie algebras, pre-Lie algebras, Leibniz algebras and 3-Lie algebras and some…

Deformation and Hochschild cohomology of coisotropic algebras

- MathematicsAnnali di Matematica Pura ed Applicata (1923 -)
- 2021

Coisotropic algebras consist of triples of algebras for which a reduction can be defined and unify in a very algebraic fashion coisotropic reduction in several settings. In this paper, we study the…

J un 2 01 8 α-type Hochschild cohomology of Hom-associative algebras and Hom-bialgebras

- Mathematics
- 2018

In this paper we define a new cohomology for multiplicative Hom-associative algebras, which generalize Hochschild cohomology and fits with deformations of Hom-associative algebras including the…

Relative Rota-Baxter systems on Leibniz algebras

- Mathematics
- 2021

In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Maurer-Cartan elements…

-Operators on Lie ∞-algebras with respect to Lie ∞-actions

- MathematicsCommunications in Algebra
- 2022

Abstract We define -operators on a Lie ∞-algebra E with respect to an action of E on another Lie ∞-algebra and we characterize them as Maurer-Cartan elements of a certain Lie ∞-algebra obtained by…

## References

SHOWING 1-10 OF 35 REFERENCES

Formal deformations of morphisms of associative algebras

- Mathematics
- 2005

The strong homotopy Lie algebra, controlling simultaneous deformations of a morphism of associative algebras and its domain and codomain is constructed. Isomorphism of the cohomology of this strong…

A New Cohomology Theory Associated to Deformations of Lie Algebra Morphisms

- Mathematics
- 2003

We introduce a new cohomology theory related to deformations of Lie algebra morphisms. This notion involves simultaneous deformations of two Lie algebras and a homomorphism between them.

Simultaneous deformations and Poisson geometry

- MathematicsCompositio Mathematica
- 2015

We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an $L_{\infty }$-algebra, which we construct explicitly. Our machinery…

The L ∞ -deformation complex of diagrams of algebras

- Mathematics
- 2009

The deformation complex of an algebra over a colored PROP P is defined in terms of a minimal (or, more generally, cofibrant) model of P. It is shown that it carries the structure of an L∞-algebra…

Higher Derived Brackets for Arbitrary Derivations

- Mathematics
- 2004

We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie…

Introduction to supergeometry

- Mathematics
- 2011

These notes are based on a series of lectures given by the first author at the school of "Poisson 2010", held at IMPA, Rio de Janeiro. They contain an exposition of the theory of super- and graded…

COHOMOLOGY AND DEFORMATIONS IN GRADED LIE ALGEBRAS

- Mathematics
- 1966

Abstract : The theories of deformations of associative algebras, Lie algebras, and of representations and homomorphisms of these all show a striking similarity to the theory of deformations of…

Deformation theory of representations of prop(erad)s I

- Mathematics
- 2009

Abstract In this paper and its follow-up [Merkulov and Vallette, J. reine angew. Math.], we study the deformation theory of morphisms of properads and props thereby extending Quillen's deformation…